
Shepherdson
2. Follows from (1) and Theorem 16.
3.
The soundness half of (3) is Theorem 25 (1), the completeness is due to
Jaffar, Lassez, and Lloyd [1983], and appears in Lloyd [1984] as
Theorem 16.1, pp.
82-83.
•
Although following Jaffar, Lassez, and Lloyd, we have called this a com-
pleteness result for negation as failure, it has nothing to do with the use of the
negation as failure rule in a computation. Since the query and the program
clauses are all totally positive, the rule of negation as failure is never invoked
in the computation. The only thing the result has to do with negation is that it
tells us when a positive query fails unde ...